Download Mapping Heat Origin in Plasmonic Structures

PRL 104, 136805 (2010)
PHYSICAL REVIEW LETTERS
week ending
2 APRIL 2010
Mapping Heat Origin in Plasmonic Structures
Guillaume Baffou,1,* Christian Girard,2 and Romain Quidant1,3,†
1
ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
2
CEMES, CNRS, Université Paul Sabatier, 29 rue J. Marvig, F-31055 Toulouse, France
3
ICREA-Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain
(Received 18 September 2009; published 2 April 2010)
We investigate the physics of photoinduced heat generation in plasmonic structures by using a novel
thermal microscopy technique based on molecular fluorescence polarization anisotropy. This technique
enables us to image the heat source distribution in light-absorbing systems such as plasmonic nanostructures. While the temperature distribution in plasmonic nanostructures is always fairly uniform because of
the fast thermal diffusion in metals, we show that the heat source density is much more contrasted.
Unexpectedly the heat origin (thermal hot spots) usually does not correspond to the optical hot spots of the
plasmon mode. Numerical simulations based on the Green dyadic method confirm our observations and
enable us to derive the general physical rules governing heat generation in plasmonic structures.
DOI: 10.1103/PhysRevLett.104.136805
PACS numbers: 73.20.Mf, 33.50.j, 44.10.+i
Gold nanoparticles can efficiently absorb visible or infrared light energy in very confined volumes, making them
ideal remotely controllable nanosources of heat. Besides
the fundamental interest of understanding nanothermodynamics phenomena, the ability to produce pointlike heat
sources opens up a wide range of applications in physics,
chemistry, and biology. For instance, gold nanoparticles as
nanosources of heat already have promising applications in
nanoscale catalysis [1], magnetism [2], microfluidics [3–
5], phononics [6,7], and medicine [8–11], such as for
photothermal cancer cell destruction or drug delivery.
However, while the physics of thermal radiative transfer
in plasmonics has been widely studied, mostly by Greffet
and co-workers [12–14], the physics of heat generation and
thermal diffusion in plasmonic nanostructures is poorly
investigated and understood mostly due to the lack of
experimental tools.
In this Letter, we investigate experimentally the physics
of heat generation in gold plasmonic nanostructures by
using a novel thermal microscopy technique. Based on
fluorescence polarization anisotropy, this technique enables us to map the heat source density within arbitrarily
complex plasmonic structures upon laser illumination with
a resolution of about 300 nm. We apply this method to two
different geometries: an elongated gold nanowire and a
gold nanorod dimer. We show that the spatial origin of heat
in the metal does not usually match the optical near-field
distribution. Simulations based on the Green dyadic technique are performed to validate our experimental data and
gain further understanding of the involved physics. Finally,
as a direct application of our method, we show that nanohole patterning is an efficient way to enhance heat generation in metals.
Let us consider a plasmonic metal structure embedded in
a condensed (fluid or solid) medium. In the steady state
regime, the heating processes inside and outside plasmonic
structures are governed by the Poisson equation [15]:
0031-9007=10=104(13)=136805(4)
r2 TðrÞ ¼ hðrÞ;
(1)
where is the thermal conductivity (either of the metal or
the surroundings), TðrÞ is the temperature distribution, and
hðrÞ represents the heat source density (HSD) that has
dimensions of a power per unit volume. For submicrometric metal structures heated by external illumination, the
HSD hðrÞ can be strongly nonuniform, depending on the
morphology of the metal structure [16]. However, despite
the nonuniformity of the heat origin hðrÞ, the temperature
TðrÞ remains quasiuniform throughout the metal due to the
very high thermal conductivity of metals compared with
that of the surroundings. For instance, the ratio between
thermal conductivity of gold and water reaches about 500.
As a consequence, thermal characterization restricted to
the steady temperature distribution TðrÞ lacks important
information compared with the heat origin hðrÞ inside the
structure [17].
The novel thermal imaging method presented in this
study is based on measuring the fluorescence polarization
anisotropy (FPA) of fluorophores dispersed in solution.
Briefly, a temperature increase tends to make the fluorescent molecules rotate faster during their fluorescence lifetime, which consequently reduces the degree of
polarization of the emitted fluorescence. In an earlier study
we showed that FPA measurements provide direct information on the distribution of the steady temperature TðrÞ
[17]. In this work, using a dual-objective setup and different illumination and scanning conditions, the technique has
been further developed to assess the HSD hðrÞ, a quantity
that provides much more information than only the knowledge of the temperature distribution TðrÞ.
The samples consist of gold nanostructures made by
e-beam lithography, lying upon glass and surrounded by
a glycerol-water (4:1) mixture in which fluorescein molecules are dispersed. The use of glycerol instead of pure
water is intended to slow down the rotational motion of the
136805-1
Ó 2010 The American Physical Society
PRL 104, 136805 (2010)
week ending
2 APRIL 2010
PHYSICAL REVIEW LETTERS
molecules to increase the sensitivity of the method.
Figure 1 presents the setup that we used to perform both
thermal (temperature and HSD) and optical (two-photon
luminescence of gold) measurements. It comprises two
illumination parts: a blue laser beam (473 nm) from the
bottom of the sample to excite the fluorescent molecules
and an infrared (IR) laser beam from the top of the sample.
This IR laser beam can be tuned between 700 and 900 nm
and switched from cw to pulsed mode. The cw mode is
used to heat the plasmonic structures while the pulsed
mode is used for the two-photon luminescence (TPL)
measurements. Using two fast steering mirrors, both laser
beams can be individually positioned and eventually raster
scanned. The sample is mounted on a piezostage that can
be raster scanned as well. All these degrees of freedom
allow us to assess different physical quantities by scanning
either the blue beam, the infrared beam, or the sample. To
obtain the steady state temperature map TðrÞ, the metal
structure of interest is illuminated by an extended (unfocused) IR light through the upper objective, the sample
stage is fixed, and the bottom blue beam is raster scanned
throughout the sample. Conversely, to measure the HSD,
the blue beam and the IR beam are both focused and
spatially overlapped while the stage is scanned. In such a
configuration, local heating and FPA probing are performed simultaneously at each scan location. In the following, we first demonstrate that the HSD is indeed the
physical quantity measured when using the later illumination and scanning conditions.
In a metal and, in particular, in a plasmonic structure
under illumination, the HSD arises from Joule effect [16]:
1
hðrÞ ¼ fj? ðrÞ EðrÞ þ jðrÞ E? ðrÞg;
2
(2)
where jðrÞ and EðrÞ are the complex amplitudes of the
electronic current density and the electric field. The relations jðrÞ ¼ i!PðrÞ and PðrÞ ¼ "0 ð"! 1ÞEðrÞ permit us
to express the HSD as a function of the electric field from
the previous equation:
hðrÞ ¼ !"0 Imð"! ÞjEðrÞj2 ;
(3)
θ, φ
Ti:Sapphire laser
700-950 nm
x, y, z
Avalanche
Photodiode
APD1
where ! is the angular frequency of light and "! is the
permittivity of the metal [18]. Using the Green function
formalism, the general solution of the temperature profile
inside the structure can be written as
Z
TðrÞ ¼
Gðr; r0 Þhðr0 Þdr0 ;
(4)
V
where the integral runs over the structure volume V,
Gðr; r0 Þ is the scalar thermal Green function associated to
the Poisson equation (1) that vanishes at infinity. Similarly,
using the Green dyadic formalism of electrodynamics
[19,20], the electric field amplitude inside the structure
reads:
Z
E ðrÞ ¼
Kðr; r0 Þ E0 ðr0 Þdr0 ;
(5)
V
0
where Kðr; r Þ is the generalized Green dyadic tensor
related to the plasmonic structure and E0 ðrÞ is the external
field exciting the structure. Under plane wave illumination,
E0 ðrÞ ¼ E0 ux , where ux is the unit vector along the x axis.
From Eqs. (4) and (5) and after introducing the complex
vector Kðr; r0 Þ ux ¼ Kx ðr; r0 Þ, the HSD distribution generated by a plane wave illumination is given by
Z
2
0
0
hPW ðrÞ ¼ !"0 Imð"! ÞE20 K
ðr;
r
Þdr
: (6)
x
V
In practice this HSD cannot be directly measured under
plane wave illumination but by scanning a finite-size light
spot, as explained above. Let us consider this light spot as a
Dirac distribution field located in r0 and defined by
E0 ðrÞ ¼ vE0 ux ðr r0 Þ, where v has dimensions of volume and can be incorporated in the volume of excitation.
The temperature distribution generated by such a local
excitation reads then:
Z
Tloc ðrÞ ¼ v2 E20
!"0 Imð"! ÞGðr; r0 ÞjKx ðr0 ; r0 Þj2 dr0 :
V
(7)
This exact solution can be simplified using two approximations. First, as mentioned above, even under local
excitation, temperature processes at the submicrometric
scale are so fast that the temperature remains quasiuniform.
As a consequence, Gðr; r0 Þ behaves as a constant G0 , and
TðrÞ can be reduced to Tðr0 Þ. In addition, after applying a
mean field approximation [21] on the volume V of the
structure to perform the spatial integrals of Kx ðr; r0 Þ and
Kx ðr0 ; r0 Þ, Eqs. (6) and (7) can be rewritten as
APD2
Dioded pumped laser
473 nm
θ, φ
FIG. 1 (color online). Schematic view of the experimental
setup.
hPW ðrÞ ¼ !"0 Imð"! ÞV 2 E20 jKx ðrÞj2 ;
(8)
Tloc ðr0 Þ ¼ v2 E20 VG0 !"0 Imð"! ÞjKx ðr0 Þj2 ;
(9)
leading to a linear relation between the HSD hPW ðrÞ obtained under plane wave illumination—the quantity we
want to measure—and the temperature Tloc ðrÞ measurement under local illumination—the quantity we actually
record in our experiment:
136805-2
PRL 104, 136805 (2010)
Figure 2 illustrates the two operational modes of the
technique on a gold nanowire. Figure 2(a) shows the
experimental measurement of the steady-state temperature
distribution TðrÞ around the gold structure while Figs. 2(b)
and 2(c) give the associated distribution of the HSD hðrÞ
for both parallel and perpendicular polarizations. As expected, while the temperature spreads out of the nanowire,
the heat origin is restricted to the metal. While this first
example is meant only to introduce the two quantities that
can be measured [TðrÞ and hðrÞ], it is already a first
indication of the counterintuitive physics of the HSD
hðrÞ: for a transverse polarization of the incident light
[Fig. 2(c)], the heat arises mainly from the extremities,
while the optical near-field enhancement is expected at
these locations precisely for the other polarization.
In order to understand this unexpected behavior and get
further insight into the physics of photoinduced heat generation in plasmonic nanostructures, we study in detail a
nanoantenna geometry consisting of two adjacent gold
nanorods [Fig. 3(a)]. This structure features a longitudinal
3=2 localized plasmon resonance centered at 850 nm
[Fig. 3(b)]. The optical near-field properties of this structure have been extensively investigated in a previous work
using TPL microspectroscopy [22] where we showed that
the TPL distribution can be directly compared to the nearfield distribution of jEj4 . HSD measurements for both
incident polarizations are presented in Figs. 3(c) and 3(d)
and compared to TPL measurements [Figs. 3(e) and 3(f)].
While under longitudinal polarization a strong optical field
concentration and enhancement is observed within the gap
region [Fig. 3(e)]; interestingly, the HSD behaves just the
opposite way [Figs. 3(c) and 3(d)]. Associated numerical simulations of the jEj4 distribution and of the HSD
[Figs. 3(g)–3(j)] support well our experimental measurements. Numerical simulations of charge [23] and current
densities are displayed in Figs. 3(k)–3(n) to bring some
further understanding: Optical hot spots usually come
from tip effect and charge accumulation at the metal interMeasurements
a
0
µm
2
2
b
1
0.6
1
Heat source density h(r)
26
c
40
d
21
21
Two-photon luminescence
100
e
112
f
0
0
µm
2
0
0
µm
2
Simulations
Heat source density
g
h
Electric near field |E(r)|4
i
Charge distribution q(r)
k
j
l
m
+
-
Current density |J(r)|
FIG. 2 (color online). (a) Steady state temperature profile
measured around a gold nanowire lying upon a glass substrate
(the wire is 200 nm wide, 35 nm thick, and 2 m long). (b),
(c) Experimental measurements of the associated heat source
density for (b) a light parallel and (c) perpendicular to the
nanowire axis This polarization is represented by the white
double arrows. The laser wavelength is 725 nm and the illuminance around 40 mW=m2 .
0.85
Wavelength (µm)
°C
(10)
counts
V
:
v G0
2
Extinction (arb. units)
hPW ðrÞ ¼ Tloc ðrÞ
week ending
2 APRIL 2010
PHYSICAL REVIEW LETTERS
n
FIG. 3 (color online). Scanning electron microscopy (SEM)
image (a) representing the structure of interest that consists of
two rods (460 nm long, 100 nm wide, and 40 nm thick) separated
by a gap of 60 nm. (b) Experimental extinction spectrum showing the longitudinal resonance at 850 m. HSD maps for
horizontal (c) and vertical (d) polarizations of the incident light
(P ¼ 3:5 mW, ¼ 850 nm). Two-photon luminescence maps
for horizontal (e) and vertical (f) polarizations of the incident
light (P ¼ 76 W, ¼ 850 nm). Associated numerical simulations using the Green dyadic tensor technique on a structure
composed of 8926 cells: heat source density (g),(h), electric near
field (i),(j), charge distribution (k),(l), and current density
distribution (m),(n).
136805-3
PRL 104, 136805 (2010)
PHYSICAL REVIEW LETTERS
FIG. 4 (color online). SEM image of two gold triangles (a)
35 nm thick. The right triangle is characterized by a nanohole
pattern. Experimental measurement of the HSD (b) showing a
higher HSD associated with the nanostructured triangle (scalebar: 500 nm).
face [Figs. 3(k) and 3(l)], whereas heat arises on the contrary from areas where charges can freely flow [Figs. 3(m)
and 3(n)]. This particular example evidences a general
rule: In plasmonic structures, the heat origin does not
usually match the optical hot spots. Note that TPL and
HSD measurements appear thus as complementary techniques to understand where the energy of a plasmonic
mode is optically and thermally released into the
surroundings.
The method we present is not restricted to sharply
resonant plasmonic nanoparticles. As an application of
our method, we show how HSD measurements can help
to design more efficient nanosources of heat in general.
Using e-beam lithography, we have designed mesoscopic
structures patterned with a lattice of nanoholes (Fig. 4). In
this particular case, we observe that the heat generation is
increased by around 40%—while the amount of gold is
actually reduced by a factor of 2. A substantial optimization is achieved by increasing the amount of interfaces to
generate electronic current everywhere inside the structures and not only at the outer boundaries. Because of its
complexity, such a nanostructuration remains difficult to
investigate numerically, while the experimental technique
we present in this Letter has no limitation concerning the
complexity of the system. This new kind of nanostructuration enables us to reduce the required heating laser power
to achieve the desired temperature and could have applications in thermal-induced heterogeneous catalysis of
chemical reactions at the nanometer scale where the surface/volume aspect ratio is known to be the important
parameter.
This research has been funded by the Spanish Ministry
of Sciences through Grants No. TEC2007-60186/MIC and
No. CSD2007-046-NanoLight.es and by the fundació
Cellex Barcelona.
week ending
2 APRIL 2010
*[email protected]
†
[email protected]
[1] L. Cao, D. Barsic, A. Guichard, and M. Brongersma, Nano
Lett. 7, 3523 (2007).
[2] W. A. Challener, C. Peng, A. V. Itagi, D. Karns, W. Peng,
Y. Peng, X. M. Yang, X. Zhu, N. J. Gokemeijer, Y.-T. Hsia,
G. Ju, R. E. Rottmayer, M. A. Seigler, and E. C. Gage, Nat.
Photon. 3, 220 (2009).
[3] G. L. Liu, J. Kim, Y. Lu, and L. P. Lee, Nature Mater. 5, 27
(2006).
[4] V. Garces-Chavez, R. Quidant, P. J. Reece, G. Badenes,
L. Torner, and K. Dholakia, Phys. Rev. B 73, 085417
(2006).
[5] X. Miao, B. K. Wilson, and L. Y. Lin, Appl. Phys. Lett. 92,
124108 (2008).
[6] L. Wang and B. Li, Phys. Rev. Lett. 101, 267203
(2008).
[7] L. Wang and B. Li, Phys. Rev. Lett. 99, 177208 (2007).
[8] S. Lal, S. E. Clare, and N. J. Halas, Acc. Chem. Res. 41,
1842 (2008).
[9] A. M. Gobin, M. H. Lee, N. J. Halas, W. D. James, R. A.
Drezek, and J. L. West, Nano Lett. 7, 1929 (2007).
[10] P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, Nano Today
2, 18 (2007).
[11] G. Han, P. Ghosh, M. De, and V. M. Rotello,
NanoBiotechnology 3, 40 (2007).
[12] Y. de Wilde, F. Formanek, R. Carminati, B. Gralak, P. A.
Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet,
Nature (London) 444, 740 (2006).
[13] G. Domingues, S. Volz, K. Joulain, and J. J. Greffet, Phys.
Rev. Lett. 94, 085901 (2005).
[14] E. Rousseau, A. Siria, G. Jourdan, S. Volz, F. Comin,
J. Chevrier, and J. J. Greffet, Nat. Photon. 3, 514 (2009).
[15] A. O. Govorov and H. H. Richardson, Nano Today 2, 30
(2007).
[16] G. Baffou, R. Quidant, and C. Girard, Appl. Phys. Lett. 94,
153109 (2009).
[17] G. Baffou, M. P. Kreuzer, F. Kulzer, and R. Quidant, Opt.
Express 17, 3291 (2009).
[18] P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370
(1972).
[19] O. J. F. Martin, C. Girard, and A. Dereux, Phys. Rev. Lett.
74, 526 (1995).
[20] C. Girard, E. Dujardin, G. Baffou, and R. Quidant, New J.
Phys. 10, 105016 (2008).
[21] This
mean field approximation
amounts to assimilating
R
R
jKx ðr0 ; r0 Þj2 dr0 and j Kx ðr0 ; r0 Þdr0 j2 . This working hypothesis is justified by the agreement with the experimental data. However, such an approximation loses validity
when considering symmetric (with respect to the charge
distribution, e.g., ‘‘þ þ’’) modes since they cannot be
excited using a plane wave, while they can be excited by
using a focused beam. In such a case, hPW equals zero
while tloc does not.
[22] P. Ghenuche, S. Cherukulappurath, T. H. Taminiau, N. F.
van Hulst, and R. Quidant, Phys. Rev. Lett. 101, 116805
(2008).
[23] R. Marty, G. Baffou, A. Arbouet, C. Girard, and R.
Quidant, Opt. Express 18, 3035 (2010).
136805-4